2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114187Let Γbe the convex set consisting of all marginal tracial states on the tensor product B \otimes B of the algebra B of nxn matrices over the complex numbers. We find necessary and sufficient conditions for such a state to be extremal in Γ. We also give a characterization of those extreme points in Γwhich are pure states. We conjecture that all extremal marginal tracial states are pure states.12 pagesOperator Algebras46L30text